Dowker spaces revisited

Ludwig, Lewis D. ; Nyikos, Peter ; Porter, John E.

Tsukuba J. Math., Tome 34 (2010) no. 1, p. 1-11 / Harvested from Project Euclid

Résumé

In 1951, Dowker proved that a space $X$ is countably paracompact and normal if and only if $X \times {\bf I}$ is normal. A normal space $X$ is called a Dowker space if $X \times {\bf I}$ is not normal. The main thrust of this article is to extend this work with regards $\alpha$-normality and $\beta$-normality. Characterizations are given for when the product of a space $X$ and $(\omega + 1)$ is $\alpha$-normal or $\beta$-normal. A new definition, $\alpha$-countably paracompact, illustrates what can be said if the product of $X$ with a compact metric space is $\beta$-normal. Several examples demonstrate that the product of a Dowker space and a compact metric space may or may not be $\alpha$-normal or $\beta$-normal. A collectionwise Hausdorff. Moore space constructed by M. Wage is shown to be $\alpha$-normal but not $\beta$-nornal.

Détail

Publié le : 2010-08-15
Classification:  $\alpha$-normal,  $\beta$-normal,  products,  Dowker,  Moore spaces,  $\alpha$-countably paracompact,  54D15